Journal of Low Temperature Physics

, Volume 167, Issue 5, pp 1004–1014

Development of Metallic Magnetic Calorimeters for High Precision Measurements of Calorimetric 187Re and 163Ho Spectra

Authors

    • Kirchhoff-Institute for PhysicsHeidelberg University
  • J.-P. Porst
    • Kirchhoff-Institute for PhysicsHeidelberg University
    • Physics DepartmentBrown University
  • S. Kempf
    • Kirchhoff-Institute for PhysicsHeidelberg University
  • C. Pies
    • Kirchhoff-Institute for PhysicsHeidelberg University
  • S. Schäfer
    • Kirchhoff-Institute for PhysicsHeidelberg University
  • D. Hengstler
    • Kirchhoff-Institute for PhysicsHeidelberg University
  • A. Fleischmann
    • Kirchhoff-Institute for PhysicsHeidelberg University
  • C. Enss
    • Kirchhoff-Institute for PhysicsHeidelberg University
  • L. Gastaldo
    • Kirchhoff-Institute for PhysicsHeidelberg University
Article

DOI: 10.1007/s10909-012-0556-0

Cite this article as:
Ranitzsch, P.C., Porst, J., Kempf, S. et al. J Low Temp Phys (2012) 167: 1004. doi:10.1007/s10909-012-0556-0

Abstract

The measurement of calorimetric spectra following atomic weak decays, beta (β) and electron capture (EC), of nuclides having a very low Q-value, can provide an impressively high sensitivity to a non-vanishing neutrino mass. The achievable sensitivity in this kind of experiments is directly connected to the performance of the used detectors. In particular an energy resolution of a few eV and a pulse formation time well below 1 μs are required. Low temperature Metallic Magnetic Calorimeters (MMCs) for soft X-rays have already shown an energy resolution of 2.0 eV FWHM and a pulse rise-time of about 90 ns for fully micro-fabricated detectors. We present the use of MMCs for high precision measurements of calorimetric spectra following the β-decay of 187Re and the EC of 163Ho. We show results obtained with detectors optimized for 187Re and for 163Ho experiments respectively. While the detectors equipped with superconducting Re absorbers have not yet reached the aimed performance, a first detector prototype with a Au absorber having implanted 163Ho ions already shows excellent results. An energy resolution of 12 eV FWHM and a rise time of 90 ns were measured.

Keywords

Neutrino massSingle beta decayElectron captureLow temperature detector

1 Introduction

It is well known that a non-zero \(\bar{\nu}_{\mathrm{e}}\) mass modifies the energy spectrum of electrons emitted in β-decays as well as a non-zero νe mass modifies the energy spectrum following an EC. The sensitivity to the neutrino mass is very high in an energy range of a few eV width located around the endpoint Q of the spectrum. The fraction of counts in the interesting narrow region ΔE around the endpoint is extremely small and approximately proportional to (ΔE/Q)3. This is the reason why nuclides with especially low Q are used for neutrino mass experiments. Besides the case of 3H, which is investigated since long time [13], two other nuclides are nowadays in the focus of neutrino physicists, the β instable 187Re [4, 5] with Qβ≃2.5 keV and the nuclide 163Ho [6] which decays through the EC channel with QEC≃2.6 keV. Due to the very low energy available for the decay, the most efficient method to measure the corresponding spectra with high precision is to use low temperature micro-calorimeters having the source contained in the absorber. This method allows for the measurement of the calorimetric spectrum, where all the energy emitted in the decay except for that taken away by the neutrino can be measured. The calorimetric measurements provide results which are not depending on decay branching ratios. We have developed low temperature metallic magnetic calorimeters [7] for high precision measurements of the calorimetric spectra of 187Re and 163Ho.

MMCs are low temperature detectors, typically operated at a temperature below 100 mK. They are composed of an energy absorber well thermally connected to a paramagnetic temperature sensor placed in an external magnetic field and weakly coupled to a thermal bath. The absorbed energy increases the temperature of the detector which leads to a change of the magnetization of the sensor. This change of magnetization is read out as a change of flux in a low-noise high-bandwidth dc-SQUID. The results achieved by MMCs, such as an energy resolution of 2.0 eV and a pulse rise-time of about 90 ns [8], motivate their use in experiments for neutrino mass investigation [9]. We discuss the status of the development of MMCs for a 187Re beta spectrum measurement and show the results obtained with the first MMC prototype with implanted 163Ho.

2 MMCs for 187Re β Spectrum Measurements

The use of superconducting rhenium absorbers is motivated by the low specific heat of the superconducting state well below the transition temperature. Nevertheless the thermalization of energy in superconducting absorbers is not trivial and leads to thermal pulses characterized by very long relaxation tails [10]. Therefore the optimization of MMCs for the precise measurement of the 187Re beta spectrum starts from the investigation of the energy thermalization in the Re absorber. The first detector prototypes, described in detail in [11], had the rhenium absorber glued with a very thin layer of Stycast 1266. It was possible to describe the pulse shape over the full temperature range and for different persistent currents in the meander-shaped coil by including an additional heat capacity. This can be justified by the presence of glue and normal metal regions in the absorber volume due to the residual magnetic field. The energy resolution ΔEFWHM achieved and the pulse rise times observed were not sufficient for a neutrino mass measurement.

The present generation of detectors, aiming to improve these two parameters, is based on an optimized design which allows to achieve an energy resolution below 5 eV and a pulse rise time in the 90 ns range when a gold absorber is used [8, 12]. A schematic of the detector layout is depicted in Fig. 1. The detector chip has a size of 3.5 mm×3.5 mm and the detector itself consists of two meander-shaped pick-up coils that form a gradiometric loop. Each meander fills a square with a side length of ls=245 μm. The two meanders can be covered with one or two paramagnetic Au:Er sensors and can be connected in parallel to the input coil of a SQUID via superconducting aluminum wire bonds from the labelled SQUID bond pads. The superconducting niobium meander circuit is not only used to read out changes in magnetization but also to store a persistent current If that provides the necessary magnetic field for the sensor. More details on the MMC detector design and fabrication can be found in [7].
https://static-content.springer.com/image/art%3A10.1007%2Fs10909-012-0556-0/MediaObjects/10909_2012_556_Fig1_HTML.gif
Fig. 1

(Color online) Schematic of the detector configuration developed for 187Re calorimetric spectrum measurement. From left to right: The design of the detector chip, some details of the double meander design and a schematic of the mounting of the Re absorber

The starting material for the rhenium absorbers was a commercially available single crystal disk with 5N purity [13] with a diameter of d=8 mm and a thickness of h=500 μm. It was cut into cuboids of approximately 240 μm×240 μm×500 μm with a wire saw. A rhenium absorber of this size provides a 187Re activity of about 0.5 Bq. One polished face of the rhenium absorber is covered with a sputter-deposited Cu(500 nm)–Au(10 nm) bilayer. This face of the absorber is diffusion-welded to the five gold stems (electro-deposited, about 5 μm thick, 30 μm diameter) grown on the sensor. In this configuration a metallic link connects absorber and sensor, and the presence of the stems reduces the loss of high energy phonons. Such a detector was characterized using an 55Fe calibration source. The measured magnetization, which reflects the thermodynamical properties of the sensor, did not show deviations from the bulk behavior, suggesting that the process of diffusion-welding does not degrade the sensor properties.

The thermal pulses following the absorption of 6 keV photons were analyzed. The rise time improved by almost two orders of magnitude. The time needed to reach 80% of the total amplitude is about 7 μs. On the other hand the amplitude of the pulses was about thirty times smaller than expected over the full working temperature range and for all the used persistent currents in the meander shaped pick-up coil. This can be seen in the Fig. 2 where on the left the expected pulse height is shown for three different persistent currents as function of temperature and on the right the corresponding measured pulse height.
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Fig. 2

(Color online) Left: Expected signal size in the first-stage SQUID per unit of energy input into the detector as a function of temperature for three field generating persistent currents. Right: Measured signal size of the detector for the same field generating currents

A possible reason to explain this observation is that a fraction (1−η) of the energy deposited by the incoming X-ray does not thermalize in the temperature sensor on the timescale in which the pulse is distinguishable from noise, and thus cannot be observed. By calculating the area under the temperature pulse we have a measurement of the energy that is seen by the sensor, ΔEth=Gb∫ΔTdt, where Gb is the thermal conductance between temperature sensor and thermal bath. The thermal pulses following the absorption of 5.9 keV photons are fitted over a period of 40 ms using a sum of exponential functions. The extracted function is then integrated from zero to infinity and using a Gb scaled from a different detector design with normal metal absorber, results in an energy of about 250 eV, which corresponds to 4% of the deposited energy. The experimental evidence seems to point towards the existence of long living states which store the energy. The microscopic interpretation of these degrees of freedom is still not clear. Possible candidates are the presence of normal metal regions due to residual magnetic field, on the level of the earth field, in the absorber volume while cooling, quasi-particles at the energy gap, phonons which do not down-convert in the characteristic time of the pulse formation and vortex as well as vortex ring structures. Presently, there is no evidence pointing to a preferred explanation.

Unfortunately, due to the reduced size of the pulses, it was not possible to resolve longer decay constants in this first measurement. To overcome this problem we characterized the same detector by using an external 241Am source, having the benefit of a gamma line at 60 keV. In this experiment we could identify a very long tail in the signal shape with a time constant of τ≃630 ms at 30 mK. The relative amplitude for the long decay is about 5% of the total pulse height. The total pulse height is 30 times smaller than expected, in agreement with the previous measurement. An averaged pulse corresponding to 60 keV photons absorbed in the rhenium at a temperature of 30 mK is shown in Fig. 3. The area under the pulse, calculated using the fit of an averaged pulse obtained over a time window of 1.2 s, and using the same thermal link Gb as in the previous measurement, corresponds to about 33 keV, more than half the deposited energy.
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Fig. 3

(Color online) Pulse shape corresponding to the absorption of a 60 keV photon in the superconducting rhenium absorber at 30 mK and with a persistent current of 60 mA. The inset shows the long tail of the pulse and superimposed the fit

In order to reduce potential systematic errors due to the use of a calculated Gb to extract the detected energy ΔEth, an interesting possibility is to simultaneously measure events in the bulk Re absorber and in a Au layer deposited onto the paramagnetic Au:Er sensor. Figure 4 shows the schematic of the detector that can measure the two different thermal pulses. This detector is based on a large area double meander with a pixel side length of 1 mm and a pitch of the meander stripes of 10 μm. A 5 μm thick Au absorber/thermalization layer is electroplated on top of the Au:Er sensor. Additionally 16 stems with a diameter of 100 μm and 7 μm height are structured on top to provide an interface for the attachment of an additional absorber. A rhenium cuboid having the same dimensions of the one used in the already described experiments, is diffusion welded onto 4 of these Au stems, covering an area corresponding to (1/16)th of the Au area. An external 55Fe source has been used for the characterization. A collimator was structured with two holes to illuminate firstly the Re cuboid and secondly the bare Au as depicted in Fig. 4.
https://static-content.springer.com/image/art%3A10.1007%2Fs10909-012-0556-0/MediaObjects/10909_2012_556_Fig4_HTML.gif
Fig. 4

(Color online) Schematic of the detector configuration to compare events in the Re absorber with events in Au. From left to right: the design of the detector chip, the particular of the double meander design and a schematic of the mounting of the Re absorber. The positions of X-ray interaction, as defined by the collimating holes are indicated by circles

By analyzing the pulses corresponding to the events in Au as function of temperature for a field generating persistent current of If=100 mA we found the expected behavior, as can be seen in Fig. 5 (left) where the theoretical expectation (line) is compared to the measured data (closed symbols). The signal amplitude (open symbols) of the events absorbed in Re are much smaller. Figure 5 (right) shows the averaged flux pulse in the SQUID on logarithmic scale, for events in Au and in Re, respectively, acquired at a temperature of 35 mK. The amplitude of the pulses for events in Re, extrapolated back to the beginning of the pulse, is a factor of 5 smaller than for events in Au while the area, calculated by integrating the fit of an averaged pulse over a time interval of 24 ms from zero to infinity, corresponds to a detected energy of ΔEth=2.6 keV which is slightly less than half the deposited energy. These results agree roughly with the one obtained in the previously discussed experiment. The longest observed decay time is τ≃44 ms at 35 mK. This long decay time is not present in pulses for Au events.
https://static-content.springer.com/image/art%3A10.1007%2Fs10909-012-0556-0/MediaObjects/10909_2012_556_Fig5_HTML.gif
Fig. 5

(Color online) Left: Pulse heights per unit energy comparing events absorbed in Re (collimator 1 in Fig. 4) and in Au (collimator 2 in Fig. 4) with simulations. Right: Pulse shape of averaged events in Au and in Re at T=35 mK with a persistent current of If=100 mA on logarithmic scale. The inset shows the first part of the pulse over 1 ms to compare the signal rise

Even if the thermal behavior is not completely reproducible from experiment to experiment, we can state that the thermalization of energy in superconducting rhenium absorbers is strongly affected by the presence of degrees of freedom able to store a large fraction of energy for long time, when deposited in the form of ionizing particles. The same energy transmitted to the rhenium absorber in a thermal (non-ionizing) form does not lead to the transfer of energy to those degrees of freedom. This is especially evident for detectors with clean metallic interfaces between rhenium absorber and sensor. On the other hand by improving the interface between rhenium and sensor we achieved fast pulse rise-times of about 7 μs, which presently represents the fastest response obtained with low temperature detectors with rhenium based absorbers. Nevertheless the fast response can not compensate the reduced signal to noise ratio. The achieved results with superconducting rhenium absorbers do not yet exhibit a detector performance as required in large scale neutrino mass experiment as MARE [14]. A better understanding of the energy thermalization in the superconducting rhenium absorber might lead to an improvement of the detector signal. A further important aspect presently under investigation are different rhenium alloys, including dilute magnetic alloys, to be used as absorber.

3 MMCs for 163Ho EC Spectrum Measurements

3.1 Experimental Details

In order to measure the calorimetric EC spectrum of the 163Ho we decided to include the source in the absorber by means of ion implantation [15]. A schematic of the detector chip developed for the first test is shown in Fig. 6. The 5 mm×5 mm large detector chip hosts four double meander shaped pick-up coils. Each of them has one meander equipped with Au:Er sensor and Au absorber, 190 μm×190 μm in area. The absorber is structured in a way that the ions can be implanted after the deposition of the first half of the absorber consisting of 5 μm of Au. After the ion implantation the absorber is completed with additional 5 μm Au. The geometry ensures a quantum efficiency for the energy emitted after the EC of 163Ho close to 100%. A complete description of the detector and the characterization of the achieved performance with respect to a detector prior to implantation is discussed in [16]. The data presented in the following correspond to the measurement of one of the four detectors with implanted 163Ho. A two-stage SQUID read-out was used (C4X1 as front-end SQUID and C3X25 as amplifier SQUID [17]). The signal was amplified by the XXF-1 SQUID electronics [18] and filtered before being acquired using a 12-bit high speed digitizer (GaGe CompuScope 12100 [19]). The detector was operated at 20 mK in a dilution refrigerator and an external 55Fe source was used for calibration.
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Fig. 6

(Color online) Schematic of the detector used for 163Ho EC spectrum measurement

3.2 Experimental Results and Analysis

The EC of 163Ho can be described by the following decay scheme:
https://static-content.springer.com/image/art%3A10.1007%2Fs10909-012-0556-0/MediaObjects/10909_2012_556_Equ1_HTML.gif
(1)
After one electron from an inner shell is captured by the nucleus, an electron neutrino is emitted and the daughter atom is left in an excited state. The de-excitation can occur through different channels: X-ray emission, Coster-Kronig transitions or Auger electrons. The calorimetric spectrum includes the measurement of the energy released in all the possible channels, therefore it represents the complementary neutrino energy spectrum. The shape of this spectrum is characterized by a sum of Lorentzian peaks, centered at the binding energy EH of the captured electron, where H represents the hole left in the orbitals (for 163Ho H can be MI, MII, NI…). Each of them has a characteristic width ΓH and amplitude given by the square of the electron wave function calculated at the origin \(\varphi _{\mathrm{H}}^{2}(0)\) corrected with the exchange and overlap correction factor BH. The calorimetric spectrum, reducing the contribution of the Fermi coupling and of the square of the nuclear matrix element to a constant https://static-content.springer.com/image/art%3A10.1007%2Fs10909-012-0556-0/MediaObjects/10909_2012_556_IEq3_HTML.gif, can be written as
https://static-content.springer.com/image/art%3A10.1007%2Fs10909-012-0556-0/MediaObjects/10909_2012_556_Equ2_HTML.gif
(2)
The parameters used to calculate the theoretical expectations are given in Table 1.
Table 1

163Dy spectral line properties compared with our observations. The amplitudes of the electron wave function at the origin \(\varphi_{\mathrm{H}}^{2}(0)\) are obtained from [20], while the exchange and overlap corrections BH from [21]. The electron binding energies \(E_{\mathrm {H}}^{\mathrm{lit}}\) are taken from [22] and the spectral line widths \(\varGamma _{\mathrm{H}}^{\mathrm{lit}}\) from [23]

Spectral line H

\(\varphi_{\mathrm{H}}^{2}(0)/\varphi_{\mathrm{MI}}^{2}(0)\)

BH

\(E_{\mathrm{H}}^{\mathrm{lit}}\ [\mathrm{eV}]\)

\(\varGamma _{\mathrm{H}}^{\mathrm{lit}}\ [\mathrm{eV}]\)

\(E_{\mathrm{H}}^{\mathrm{exp}}\ [\mathrm{eV}]\)

MI

1

1.083

2047

13.2

2039

MII

0.0507

1.031

1842

6

1837

NI

0.232

1.151

414.2

5.4

410

NII

0.0115

1.108

333.5

5.3

327

Figure 7 shows the spectrum acquired in about 3 days of measurement time with a superimposed fit obtained by convolving the theoretical calorimetric spectrum given in (2) with a Gaussian distribution representing the line shape of the detector. In this fit the QEC value was set to 2.8 keV which is the best value discussed in the following and only two parameters were left free, a global count rate scaling factor and the Full Width at Half Maximum (FWHM) of the detector line shape, which was determined to be ΔEFWHM=12 eV by this fitting. The lines corresponding to the transition MI, MII, NI, NII can be clearly distinguished. The spectrum was cut below 100 eV due to the large background and difficulties in pulse discrimination. Additional lines are present in the spectrum and originate from the EC of 144Pm which was ion-implanted together with the 163Ho since it was mass selected as a fluoride. For this measurement, the spectrum of 144Pm represents the largest source of background. On the other hand the presence of additional lines in the energy region around 1.5 keV made it possible to achieve a more precise energy calibration for the 163Ho spectrum. Using this energy calibration, each of the lines was separately fitted and we could extract the best value for the binding energy. The last column of Table 1 reports the measured binding energies. The experimentally found energies agree well with literature values, within precision of the used detector. Enhanced binding energy shifts in the range of ΔE∼20 eV as reported earlier [24, 25] were not observed.
https://static-content.springer.com/image/art%3A10.1007%2Fs10909-012-0556-0/MediaObjects/10909_2012_556_Fig7_HTML.gif
Fig. 7

(Color online) Calorimetric spectrum of 163Ho as measured (black histogram) and fitted (green area). The origin and the parameters of the fit are described in the text

From the analysis of the measured spectrum we could evaluate a value for the endpoint energy QEC that fits the spectrum best. In fact, by looking at (2), the intensities of the de-excitation lines are modulated by the phase space factor which, for a massless neutrino, depends only on the QEC-value. The QEC-value can then be extracted by determining the ratio between the number of counts in the MI line and the NI line. These lines have the benefit to have the largest number of counts and to be very close to the endpoint of the spectrum and relatively far away from the endpoint, respectively. The endpoint energy can then be extracted by using the measured parameters of the lines MI and NI and the theoretical line intensities obtained from the spectral shape given in (2):
https://static-content.springer.com/image/art%3A10.1007%2Fs10909-012-0556-0/MediaObjects/10909_2012_556_Equ3_HTML.gif
(3)
where WH is the experimental number of counts in the spectral line H, being evaluated after subtracting the background. The error was larger in particular for the NI line which is very close to the NII line and to atomic de-excitation lines of 144Pm. In addition the measured spectrum contains a number of additional counts on the high energy side of the NI line of unknown origin. Similarly, additional counts above the NI line can be seen in the calorimetric spectrum discussed in [25]. Another potential systematic error in the evaluation of WH is the presence of a low energy tail of the lines due to the escape of high energy phonons. This problem will be avoided in future detectors by the implementation of stems between absorber and sensor. Using the values for BH and for φH(0)2 given in Table 1, the best value for the QEC is:
$$Q_{\mathrm{EC}}=(2.80\pm0.08)~\mathrm{keV}.$$
(4)
In the evaluation of the error we considered the quantities BH and φH(0)2 to be free of uncertainties. Within this error, the value of QEC extracted as described from our measurements is not compatible with the value QEC=(2.555±0.016) keV [26] obtained by averaging several atomic mass measurements, but agrees well with the one derived from the calorimetric measurements described in [25]. Assuming that we have not underestimated any potential systematic error in our experiment, and taking the agreement among the calorimetric measurements as well as the disagreement to the mass measurements serious, we need to conclude, that our present knowledge of the parameters BH and φH(0)2, is not sufficient to describe the discussed calorimetric spectra. In fact, the available values for these parameters strongly depend on theoretical calculations. Taking the spread of those values as uncertainty, one might even be able to derive a QEC from the presented measurements that agrees within the errors with the one of mass measurements.

In any case, the discussion of the calorimetric spectrum presented here clearly points out, that all the three aspects—the calorimetric measurement, the atomic mass measurement and the theoretical calculations—need to be revisited, in order to agree on a value on the sub-eV level for QEC, which will be of outmost importance for consistency checks in a future neutrino mass measurement.

4 Conclusion

We presented the results obtained with newly developed MMCs for the measurement of calorimetric β and EC spectra on low energy decaying nuclides. We discussed the difficulties in reaching high energy resolution using superconducting Re absorbers. The main reason is presently the incomplete thermalization of the energy deposited in the absorber via ionizing particles during the formation time of the thermal pulse. This leads to a reduced signal size and therefore to a reduced signal to noise ratio. We attribute this evidence to the storage of a large fraction of energy in long living excitations. Presently, we cannot define the type of excitations involved. On the other hand we have been able to achieve pulse rise time of order of 7 μs, which is by far the fastest response achieved with low temperature detectors featuring a Re absorber. Nevertheless the present status does not suggest the use of superconducting rhenium absorbers for high energy resolution measurements of 187Re calorimetric spectrum. We rather propose the test of Re alloys with high Re content.

Furthermore, we presented a first calorimetric spectrum of the EC of 163Ho measured with a metallic magnetic calorimeter. The 163Ho was ion-implanted directly into the absorber of the detector. This proved to be a very successful way to introduce the source in the absorber and did not influence the detector performance. The energy resolution was ΔEFWHM=12 eV, which presently represents the highest precision with which the calorimetric spectrum of 163Ho has been measured. Within the precision of the detector we could exclude large energy shifts for the position of the lines as it was previously measured. We provided our best value for the endpoint energy, in the limit of massless neutrinos QEC=(2.80±0.08) keV with the indetermination due to the reduced statistics. In this measurement the largest background contribution was given by the events from the EC of 144Pm, a contaminant implanted together with 163Ho. This problem can be solved by the production of a high purity 163Ho source. The good results obtained in this first experiment motivated the formation of the ECHO (Electron Capture HOlmium experiment) Collaboration [27]. The aim of ECHO is to combine the precise measurement of the QEC by means of newly developed high resolution Penning Traps [28] with the development of high energy resolution MMC arrays having a high purity 163Ho source [29] in the absorber and with theoretical calculations and dedicated atomic physics measurements to define a more accurate shape of the 163Ho calorimetric spectrum. The first aim of this collaboration is to measure a first high statistic spectrum with middle-to-large detector arrays and, together with a better knowledge of the theoretical spectrum, reach a sensitivity on the electron neutrino mass of a few eV.

Acknowledgements

Part of this work was supported by the “FRONTIER” fonds of Heidelberg University. The 163Ho ion-implantation was performed at ISOLDE-CERN. We would like to thank Dr. Karl Johnston and Dr. Alexander Herlert for having made the ion-implantation possible. Finally we would like to thank Prof. Yuri Novikov and Prof. George Seidel for fruitful discussions.

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